A method of the kind mentioned above is known from German patent DE 3,627,676 A1 and is used for filtering a distorted signal, e.g. an audio signal, and to equalize said signal in predetermined frequency ranges. For that purpose, an analog signal is transformed into a sequence of discrete digital values which are filtered and, if desired, thereupon again retransformed into a analog signal. In the processing of the digital values in a digital computer, diametrically opposed demands are made which are difficult to satisfy simultaneously. For instance, the processing speed should be very high in order to enable the real time processing of high-frequency signals. This, however, can only be obtained by using simple filter structures requiring a minor amount of computation. On the other hand, the selectivity of the filter should be high which, in turn, is only possible with complex filter structures, i.e. with filters of a higher order, and with a correspondingly large amount of computation.
In the method described in the aforementioned German patent DE 3,627,676 A1, first-class and second-class all-pass filters are used for the design of so-called wave digital filters. The all-pass filters differ by at least one order, i.e. the second-class all-pass filter has the order of two, when the first-class all-pass filter has the order of 1. But all-pass filters of higher order can also be used. By applying the frequency transformation known from the digital filter technique, all-pass filters for the next higher order from the first-class as well as second-class all-pass filters can be derived, the order of which is determined by the frequency transformation used.
When there is only one first-class and second-class all-pass filter in a filter arrangement, the frequency range defined by the scanning theorem is separated in two sub-bands. When additionally thereto all-pass filters of a higher order are used, the number of the sub-bands is increased and thereby an improved selection of the filtering is achieved. It is commonly known that the amount of computation for the filtering is increased by an all-pass filter of increasing order, since more extensive and consequently more time-consuming computation steps must be carried out than for filters of a lower order. In the known method, for the separation in a predetermined number of identically large sub-bands, the all-pass filters are combined in cascading stages in such a way that the required number of all-pass filters of higher order is larger than the number of all-pass filters of lower order. This results in the fact that the filtering is time-consuming.